Extreme Relativistic Electron Fluxes at Geosynchronous Orbit N. P. Meredith 1, R. B. Horne 1, J. Isles 1 and J. V. Rodriguez 2,3 1 British Antarctic Survey; 2 University of Colorado Boulder; 3 National Geophysical Data Center, Boulder ESWW12, Ostend, Belgium 23 rd -27 th November 2015

Motivation Satellite operators, designers and insurers are interested in extreme space weather events to help them better understand the satellite environment and assess the impacts of an extreme event

Motivation Satellite operators, designers and insurers are interested in extreme space weather events to help them better understand the satellite environment and assess the impacts of an extreme event The objective of this study is to calculate the electron flux for the 1 in 10, 1 in 50, and 1 in 100 year space weather event at geosynchronous orbit

Data Analysis Use GOES E > 2 MeV electron data from 1 st January 1995 to 30 th June 2014 Study uses data from GOES 8, 9, 10, 11, 12, 13 and 15 Use 5 minute resolution E > 2 MeV electron data from NOAA Typical Orbital Parameters Altitude: 35,800 km Inclination: 0 o credit: NOAA

Data Analysis Electron data have been corrected for proton contamination for the first time the data have been corrected for dead time dead time correction ranges from a factor of for fluxes around 5000 cm -2 s -1 sr -1 to ~2 for the largest fluxes observed Typical Orbital Parameters Altitude: 35,800 km Inclination: 0 o credit: NOAA

Exclude Solar Proton Events The E > 2 MeV electron data may be contaminated during solar proton events We adopt the NOAA SWPC definition of a solar proton event and exclude the electron data whenever the flux of E > 10 MeV protons is greater than 10 cm -2 s -1 sr -1 Calculate daily average when > 90% of the day has good quality data in the absence of contamination from solar protons

Primary Geographic Longitudes GOES satellites operate at two primary geographic longitudes, GOES East at 75 o and GOES West at 135 o W The satellites are at different magnetic latitudes with GOES East at 11 o N and GOES West at 4 o N GOES East and GOES West are at different L shells Since the flux of energetic electrons generally decreases with L near geosynchronous orbit we conduct our analysis for GOES East and West separately Figure adapted from Onsager et al., 2004 GOES East 75 o W λ m ~ 11 o N GOES West 135 o W λ m ~ 4 o N GOES East GOES West

Good Quality Data Points In total there are 5844 good quality data points at GOES West, corresponding to approximately 16 years of operational data There are 5649 good quality data points at GOES East corresponding to approximately 15.5 years of operational data

GOES West: E > 2 MeV Electrons

Exceedance Probability Probability that an individual sample J is greater than j (P[J>j])

Exceedance Probability Probability that an individual sample J is greater than j (P[J>j]) Flux that is exceeded 0.1% of the time is 4.5x10 4 cm -2 s -1 sr -1 at GOES East 1.35x10 5 cm -2 s -1 sr -1 at GOES West

Exceedance Probability Fluxes at GOES West are typically a factor of 2.5 higher than those at GOES East This is largely due to the fact that the satellite at GOES West is at a lower magnetic latitude and hence L shell

Extreme Value Analysis Two main methods for extreme value analysis block maxima exceedances over a high threshold For comparison with earlier work (e.g., Koons [2001]) we use the exceedances over a high threshold method For this approach the appropriate distribution function is the Generalised Pareto Distribution (GPD)

Generalised Pareto Distribution The GPD may be written in the form G(x-u) = 1 – (1+ ξ(x-u)/σ) -1/ξ where: x are the data values above the chosen threshold u ξ is the shape parameter which controls the behaviour of the tail σ is the scale parameter which determines the dispersion or spread of the distribution The GPD is a distribution function 1-G(x-u) representing the probability that a random variable X exceeds some value x given that it already exceeds a threshold u

Declustering Values can exceed the threshold on consecutive days The statistical analysis assumes that the individual exceedances are independent Technique to deal with this is known as declustering

Declustering Use an empirical rule to define clusters of exceedances and consider cluster to be active until 3 consecutive daily averages fall below the threshold Identify the maximum excess in each cluster and assume cluster maxima to be independent, with conditional excess given by the GPD Fit the GPD to the cluster maxima

Quality Checks We may assess the quality of a fitted GPD model by comparing the empirical and modelled probabilities and quantiles If the GPD model is a good method for modelling the exceeedances then both the probability and quantile plots should be linear

Return Levels The return level, x N, which is exceeded on average once every N years can be expressed in terms of the fitted parameters σ and ξ as: x N = u + (σ/ξ)(Nn d ζ) ξ – 1)) where ζ = n c /n tot, the number of cluster maxima divided by the total number of data points and n d = is the average number of data points in any given year

GOES West: Extreme Value Analysis The probability and quantile plots are both approximately linear showing that the GPD is a good method for modelling the exceedances P[X>x|X>u]Exceedances

GOES West: Return Level Plot One in Ten Year Flux 1.84x10 5 cm -2 s -1 sr -1

GOES West: Return Level Plot One in Ten Year Flux 1.84x10 5 cm -2 s -1 sr -1 One in One Hundred Year Flux 7.68x10 5 cm -2 s -1 sr -1

GOES West: Return Level Plot Largest observed flux is a one in fifty year event

GOES East: Extreme Value Analysis The probability and quantile plots are both approximately linear showing that the GPD is a good method for modelling the exceedances P[X>x|X>u]Exceedances

GOES East: Return Level Plot One in Ten Year Flux 6.53x10 4 cm -2 s -1 sr -1

GOES East: Return Level Plot One in Ten Year Flux 6.53x10 4 cm -2 s -1 sr -1 One in One Hundred Year Flux 3.25x10 5 cm -2 s -1 sr -1

GOES East: Return Level Plot Largest observed flux is a one in fifty year event

Return Levels for Event with same Frequency as the Carrington Event Largest space weather event of the last 200 years is widely regarded to be the Carrington event of 1859 When ranked by 5 different space weather effects it is the only event to appear at or near the top of each ranking [Clilver and Svalgaard, 2004] Historical auroral records suggest the return period of a Carrington type event is 150 years [Lloyds, 2013] The return levels for a 150 year event are 9.86x10 5 and 4.35x10 5 cm -2 s -1 sr -1 at GOES West and GOES East respectively Carrington, 1859

Comparison with Koons [2001] Study Our results are significantly larger than those presented in Koons [2001] The 1 in 10 year event at GOES West is about a factor of 2.7 times that estimated by Koons [2001] For more extreme events, the 1 in 100 year event at GOES West is about a factor of 7 times that estimated by Koons [2001] Meredith et al., 2015 Koons, data

July/August 2004 Largest E > 2 MeV flux of 4.91x10 5 cm -2 s -1 sr -1 observed at GOES-West on 29 th July 2004 Coincided with the largest E > 2 MeV flux of 1.93x10 5 cm -2 s -1 sr -1 at GOES-East Independent measurements of this extreme flux event suggests the flux event is real GOES-West flux exceeded 10,000 cm -2 s -1 sr -1 for nine consecutive days from 28 th July to 5 th August

July/August 2004 Double Star TC1 and TC2 reported over 30 anomalies during the period from 27 July to 10 August [Han et al., 2005] These anomalies largely occurred in the Earth’s radiation belt and were attributed to internal charging [Han et al., 2005] Han et al., JSR, 2005

July/August 2004 On 3 August, during the extended period of enhanced E > 2 MeV electron fluxes, Galaxy 10R lost its secondary xenon ion propulsion system [Choi et al., 2011] This reduced its lifetime significantly resulting in an insurance payout of US $75.3 M Galaxy 10 R secondary XIPS failure E > 2 MeV electrons

What Caused the Extreme Event ? Three consecutive storms IMF Bz remained southward for significant periods during recovery phase of each storm Average value of AE index around 900 nT for first 10 hours of each recovery phase Such high and sustained levels of AE are likely to be associated with strong and sustained levels of whistler mode chorus elevated seed electrons strong acceleration of electrons to relativistic energies Galaxy 10 R secondary XIPS failure E > 2 MeV electrons

Conclusions The daily average flux of E > 2 MeV electrons measured at GOES West is typically a factor of 2.5 higher than that measured at GOES East The 1 in 10, 1in 50 and 1 in 100 year event at GOES West are 1.84x x10 5 and 7.68x10 5 cm -2 s -1 sr -1 respectively

Conclusions The daily average flux of E > 2 MeV electrons measured at GOES West is typically a factor of 2.5 higher than that measured at GOES East The 1 in 10, 1in 50 and 1 in 100 year event at GOES West are 1.84x x10 5 and 7.68x10 5 cm -2 s -1 sr -1 respectively These flux levels can serve as “yardsticks” or “benchmarks” to compare against current or previous space weather conditions

Conclusions The daily average flux of E > 2 MeV electrons measured at GOES West is typically a factor of 2.5 higher than that measured at GOES East The 1 in 10, 1in 50 and 1 in 100 year event at GOES West are 1.84x x10 5 and 7.68x10 5 cm -2 s -1 sr -1 respectively These flux levels can serve as “yardsticks” or “benchmarks” to compare against current or previous space weather conditions The results can be used to determine the return period of any given event our results suggest that the largest event seen during the study period was a one in fifty year event

The research leading to these results has received funding from the European Union Seventh Framework Programme (FP7/ ) under grant agreements number (SPACESTORM) and is also supported in part by the UK Natural Environment Research Council Acknowledgements

GOES West: E > 2 MeV Electrons

GOES East: E > 2 MeV Electrons

Top Ten Flux Events at GOES West Flux (cm -2 s -1 sr -1 )Date 14.92x th July x th July x th July x th May x th May x th September x th September x th September x th May x th April 2006

Top Ten Flux Events at GOES East Flux (cm -2 s -1 sr -1 )Date 11.93x th July x th July x th September x th September x st July x th May x th April x th May x th September x st September 2005

Appendix 1 - Exclusions The E > 2 MeV electron data may be contaminated during solar proton events We adopt the NOAA SWPC definition of a solar proton event and exclude the electron data whenever the flux of E > 10 MeV protons is greater than 10 cm -2 s -1 sr -1 Calculate daily average when > 90% of the day has good quality data in the absence of contamination from solar protons

Appendix 1 - Exclusions We also exclude data from GOES 10 in February 2010 during a period of anomalously low fluxes attributed to count rates that had not been properly converted to fluxes [Su et al., 2014] data from GOES 12 collected in September 2003 due to a 1.5 day offset between the 5 minute and 1 minute averages data from GOES 12 after 28 November 2008 due to partial failure of the dome detector

Appendix 2 - Look Direction The single set of electron sensors on each of GOES 8-12 look westward with the exception of those on GOES 10 which looked eastward There are two sets of electron sensors on GOES-13 and GOES 15. One set looks eastward and the other looks westward. In orbit GOES 13 is upright and we select data from the westward facing telescope GOES 15 undergoes a yaw flip twice a year at the equinoxes which means the eastward looking telescope then looks westward and vice versa The manoeuvre lasts approximately half an hour and is discounted from the analysis We select the data from the appropriate westward facing channel for our analysis

Appendix 3 - Missing Satellite Location The geographic longitude of the satellite is occasionally missing in the archived files when the data are of good quality We inspected the data and found 20 intervals of missing geographic longitudes With the exception of one missing interval the satellite was parked at a particular location For the other missing interval, which lasted one day, GOES 15 was in the process of moving from 90 W to 135 W at about 1 degree a day To obtain the satellite longitude during the missing intervals we linearly interpolate between the recorded longitudes before and after the missing intervals

Appendix 4 - Yaw Flips GOES 15 undergoes a yaw flip twice a year at the equinoxes The manoeuvre lasts approximately half an hour Dates of yaw flips: September 22, 2011 c (upright) March 20, 2012 c (inverted) September 20, 2012 c (upright) March 20, 2013 c (inverted) September 23, 2013 c (upright) March 20, 2014 c (inverted) The EPEAD telemetry channels labeled ‘E’ look westward when the spacecraft is upright (yaw flip flag = 0) and eastward when the spacecraft is inverted (yaw flip flag = 1). The EPEAD telemetry channels labeled ‘W’ look eastward when the spacecraft is upright (yaw flip flag = 0) and westward when the spacecraft is inverted (yaw flip flag = 1).

20000 cm -2 s -1 sr -1 (cm -2 s -1 sr -1 ) cm -2 s -1 sr -1 (cm -2 s -1 sr -1 ) cm -2 s -1 sr -1 (cm -2 s -1 sr -1 ) cm -2 s -1 sr -1 (cm -2 s -1 sr -1 ) 1 in 10 year1.64x x x x in 50 year3.75x x x x in 100 year5.33x x x x cm -2 s -1 sr -1 (cm -2 s -1 sr -1 ) cm -2 s -1 sr -1 (cm -2 s -1 sr -1 ) cm -2 s -1 sr -1 (cm -2 s -1 sr -1 ) cm -2 s -1 sr -1 (cm -2 s -1 sr -1 ) 1 in 10 year5.85x x x x in 50 year1.23x x x x in 100 year1.67x x x x10 5 GOES West GOES East Appendix 5 – Sensitivity to Threshold Selection

Appendix 6 - Choice of Threshold at GOES West We want to fit to the GPD to the extreme values of the distribution Need enough points for a meaningful fit Quantile plot should be approximately linear For GOES West we set the threshold 4.0x10 4 cm -2 s -1 sr -1

For GOES East we set the threshold at 1.35x10 4 cm -2 s -1 sr -1 Appendix 6 - Choice of Threshold at GOES East

Appendix 7 - Is the Distribution Bounded ? The shape parameter controls the behaviour of the tail if ξ < 0 the distribution has an upper limit if ξ > 0 the distribution has no upper limit The shape parameters for the fits at GOES West and GOES East are 0.61±0.44 and 0.73±0.33 Our results suggest that there is no upper limit to the flux of E > 2 MeV electrons at geosynchronous orbit

Appendix 7 - Is the Distribution Bounded ? Early work by Koons [2001] and O’Brien et al. [2007] suggests that the flux of E > 2 MeV electrons tends to a limiting value We repeated our analysis using log fluxes as done by Koons [2001] and O’Brien et al. [2007] The new shape parameters became 0.019±0.28 and 0.16±0.23 The shape parameters for both log fits include negative values within their error bars suggesting that we treat the conclusion that the fluxes have no upper bound with caution

Appendix 7 - Is the Distribution Bounded ? The studies demonstrate the difficulty of determining the presence or absence of an upper bound from only years data A definitive answer probably requires data covering many more decades In reality there is likely to be an upper bound set by some physical process but this is not evident from the statistical analysis here